Is it possible to merge two sets such that all references to both sets will refer to the new?

They currently all are referencing to their respective sets A or B, according to the assignments you've made. For instance in the case of bRef1:

id(B)
# 112140097128

id(bRef1)
# 112140097128

The fact that the original set is modified or not by modifying the new sets depends on the kind of operations you perform. If you perform an in-place operation, for instance:

bRef1 |= {5}

And check the original variable B, you can see that indeed it has been updated:

print(B)
# {2, 4, 5}

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Though when you merge both sets, unless you also perform an in-place operation and hence explicitly update one of the two sets, you will be creating a new object:

new_set = aRef2 | bRef2

id(new_set)
# 112140098248

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But still, in the case you update in-place one of the sets A or B by merging it with the other, given that you've started out with 2 different objects, there is no way of changing that into all sets referencing the same object.